This 2026 arXiv preprint (not yet peer-reviewed) deploys five finite-temperature nuclear equations of state in 3D neutrino-magnetohydrodynamic simulations of a single 35 solar-mass, rapidly rotating progenitor. The low-T/|W| instability emerges across all models, yet its onset, dominant m=1 or m=2 spiral mode, lifetime, and emitted frequencies shift systematically with proto-neutron-star compactness and stiffness. Because the study fixes the progenitor and rotation profile, it isolates EOS effects more cleanly than earlier axisymmetric or non-rotating runs, but cannot yet address how progenitor-to-progenitor variations in angular momentum or magnetic-field topology would modulate the same instability. The reported correlation between dominant gravitational-wave frequency and effective nuclear stiffness supplies a potential multimessenger diagnostic that earlier analytic work on the low-T/|W| instability (e.g., Ott et al. 2012, Phys. Rev. D) could only forecast qualitatively. Complementary neutrino-luminosity modulations near the equator further link microphysical pressure support to observable signals, an aspect downplayed in purely hydrodynamic explorations of the same instability. Limitations remain stark: only one progenitor mass and rotation rate were examined, neutrino transport approximations affect cooling rates, and magnetic fields are included but not varied. If future LIGO-Virgo-KAGRA or third-generation detectors record a galactic core-collapse event with both gravitational-wave and neutrino data, the frequency shift documented here could discriminate between soft and stiff EOS families in a manner orthogonal to the usual post-merger or cooling neutron-star radius constraints. The preprint therefore tightens the long-sought bridge between laboratory nuclear physics and the most energetic transients in the universe.